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This live chassis issue is very common, and very old. The description of the touch sensation as like a surface roughness is dead on, too! The problem stems from the fact that the actual power supply (in the mains adapter) is completely floating with respective to the earth ground. There is a very small capacitive coupling from both sides of the supply to the chassis, essentially making a voltage divider that places the chassis at half the mains voltage above ground. In the UK, that's roughly 120 volts AC, and would be disasterous, if the voltage divider's source impedance wasn't extremely high. As it is, all you feel is a slight tingling. It's harmless but annoying, and some people will not notice it, at all. As you all have found, grounding the case with the proper adapter cord will always eliminate the problem. Oh - and it has nothing to do with the battery actually charging; even if you have a fully charged battery, having the laptop connected to the mains adapter is all that's needed...
Dave